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A cylindrical tube of length L has inner radius a while outer radius b. What is the resistance of the tube between its inner and outer surfaces? [The resistivity of its material is $ρ$ ]

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$ρ (2 πL) \ln (\frac{b}{a})$

$\frac{p}{2 πL} \ln (\frac{b}{a})$

$\frac{p}{2 πL} \ln (\frac{2 b}{a})$

$\frac{p}{πL} \ln (\frac{b}{a})$

answer is B.

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Detailed Solution

Resistance of thin elementary cylindrical shell is $dR = \frac{ρ (dr)}{2 πrL}$
$R_{total} = \int dR = \frac{ρ}{2 πL} \int_{a}^{b} \frac{dr}{r} = \frac{ρ}{2 πL} \ln \frac{b}{a}$

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